61.

A line makes the same angle θ, with each of the x and z-axis. If the angle β, which it makes with y-axis, is such that sin²β = 3sin²θ , then cos2θ equals 

• 2/3

• 1/5

• 3/5

• 3/5

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

• 3/2

• 5/2

• 7/2

• 7/2

A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by

• (3a, 3a, 3a), (a, a, a)

• (3a, 2a, 3a), (a, a, a)

• (3a, 2a, 3a), (a, a, 2a)

• (3a, 2a, 3a), (a, a, 2a)

If the straight lines x = 1 + s, y = –3 – λs, z = 1 + λs and x = t/ 2 , y = 1 + t, z = 2 – t with parameters s and t respectively, are co-planar then λ equals

• –2

• –1

• -1/2

• -1/2

The intersection of the spheres x² +y² +z² + 7x -2y-z =13 and x² +y² +z² -3x +3y +4z = 8 is the same as the intersection of one of the sphere and the plane

• x-y-z =1

• x-2y-z =1

• x-y-2z=1

• x-y-2z=1

Let  be three non-zero vectors such that no two of these are collinear. If the vector  is collinear with is collinear with  (λ being some non-zero scalar) then  equals

• λ

• λ

• λ

• λ

A particle is acted upon by constant forces  which displace it from a point  The work done in standard units by the forces is given by 

• 40

• 30

• 25

• 25

• all values of λ

• all except one value of λ

• all except two values of λ

• all except two values of λ

Let  be such that  If the projection   is equal to that of  are perpendicular to each other then  equals

• 2

• 
• 
• 

Let  be non-zero vectors such that  If θ is the acute angle between the vectors  then sin θ equals

• 1/3

• 

• 2/3

• 2/3